Progressive power lens

ABSTRACT

An additional aspherical surface amount is defined by a sum of the optimum amount at a distance portion and the optimum amount at a near portion on a progressive refractive surface. Assuming that the ratio is taken as α:β, the additional aspherical surface amount is added to the progressive refractive surface in such a manner that α and β satisfy a relationship of α+β=1. With this configuration, in the case where an aspherical shape is added to a progressive power lens for correcting visual acuity for the purpose of improving the optical performance and thinning the lens, the optimum aspherical shape can be given not only to a region along a main meridian line but also to the whole of the progressive refractive surface.

TECHNICAL FIELD

The present invention relates to a progressive power lens for correctingvisual acuity, and particularly to a design of an aspherical progressivepower lens intended to improve the optical performance of the lens andto thin the lens.

BACKGROUND ART

In recent years, various attempts have been made to improve the opticalperformances of progressive power lenses. In particular, attention isbeing given to a progressive power lens produced on the basis ofaspherical design. This is intended to compensate for an error portionof a lens caused by spherical design by assuming a condition equivalentto an actual condition under which a user wears spectacles in each ofwhich the lens is assembled, and calculating the dioptric power,astigmatism, prism, etc. of the lens by means of ray tracing.

A progressive refractive surface is originally formed by smoothlyconnecting spherical surfaces at distance and near portions, which aredifferent in curvature, to each other within one surface, and therefore,it is naturally an aspherical surface. However, the wording “theaspherical design of a progressive power lens” used in this descriptionmeans that even a point, having a specific curvature, of a progressiverefractive surface, such as a distance optical center or near opticalcenter is a aspherical surface.

A progressive power lens produced on the basis of such an asphericaldesign is disclosed in Japanese Patent Publication No. Tokko-hei2-39768, which lens exhibits effects of reducing astigmatism andthinning the lens as compared with a lens produced on the basis ofspherical design.

In the case of designing and producing a lens in accordance with thetechnique disclosed in Japanese Patent Publication No. Tokko-hei2-39768, however, there occur several problems or insufficient points.

At first, Japanese Patent Publication No. Tokko-hei 2-39768 disclosesthe structure of only a region, in the vicinity of a main meridian lineextending between distance and near portions, of the progressive powerlens. The main meridian line of a progressive power lens is certainly asimportant as to be called a main convergence line; however, it is only aline. When acquiring viewing information, a human being takes a sight ofa wide area other than the meridian line.

At second, since the dioptric power of a progressive power lens differsbetween different positions of the lens, an ideal additional asphericalsurface amount added to an original progressive refractive surface mustdiffer depending on a position of the lens. In accordance with thetechnique disclosed in Japanese Patent Publication No. Tokko-hei2-39768, the additional aspherical surface amount differs between thedistance and near portions disposed along the main meridian line;however, it is unclear what aspherical surface is set at other portions.

The region disposed along the main meridian line also includes aprogressive portion in which a focal power is continuously changed, andit is theoretically required to give an additional aspherical surfaceamount to such a progressive portion. At the present day, however, anyprior art intended to give an additional aspherical surface amount tothe above progressive portion has been not disclosed.

The progressive surface of a progressive power lens is required to beconfigured such that refractive surfaces at all portions of the lens areoptically continuous to each other within one surface. If a lens isconfigured such that although refractive surfaces at portions along themain meridian line form an optically continuous aspherical shape, therefractive surfaces at other portions not along the main meridian linedo not form an optically continuous aspherical shape, it is useless toproduce the lens on the basis of the aspherical design. As a method forforming the refractive surfaces at the portions not along the mainmeridian line into an optically continuous aspherical shape, there isknown only a method of interpolating a curvature in the directionextending, perpendicular to the main meridian line, from each point ofthe optically continuous aspherical portion along the main meridianline. It is not regarded that such a method is able to form the portionsnot along the meridian line into an ideal aspherical shape.

The production of a custom-made progressive power lens for spectacles isrequired to simply form a progressive aspherical shape on the basis ofthe optimum aspherical design for achieving effects of reducingastigmatism in accordance with the user's recipe including the dioptricpower of the lens and of thinning the lens.

In view of the foregoing, the present invention has been made, and anobject of the present invention is to provide a progressive power lensin which all of portions including a progressive portion are formed intoan optimum aspherical shape on the basis of a simple lens design.

DISCLOSURE OF INVENTION

To achieve the above object, the present invention provides aprogressive power lens in which the optimum aspherical shape is given tothe entire lens including a progressive portion by a lens design capableof simply forming a new progressive aspherical refractive shape on thebasis of a progressive spherical refractive shape, or by a lens designcapable of simply forming, on the basis of a progressive asphericalrefractive shape adapted for a certain user's recipe, a new progressiveaspherical refractive shape adapted for another desired user's recipe.

To be more specific, an additional aspherical surface amount for eachuser's recipe is not determined on the basis of ray tracing but isdetermined by a method wherein the optimum additional aspherical surfaceamount is previously determined by actual ray tracing for severalexamples selected from a range of user's recipes using a common basicprogressive refractive surface, and then an additional asphericalsurface amount for a desired user's recipe is determined byinterpolation on the basis of the optimum additional aspherical surfaceamount.

The present invention provides a progressive power lens designed on thebasis of the following five methods of calculating an additionalaspherical surface amount.

According to a first invention there is provided a progressive powerlens characterized in that at least one of two refractive surfacesforming a spectacle lens has a progressive refractive surface includinga FL distance portion and a near portion having different focal powers,and a progressive portion having a focal power progressively changedbetween the distance and near portions; coordinates are defined suchthat, assuming that the progressive refractive surface of the lensassembled in each of spectacles is viewed from the front side of a user,the horizontal direction is taken as an X-axis; the vertical direction(direction between the distance and near portions) is taken as a Y-axis;the depth direction is taken as a Z-axis; and a progressively changestarting point located at the lower end of the distance portion is takenas an origin (x, y, z)=(0, 0, 0); assuming that a coordinate of anoriginal progressive refractive surface is taken as z_(p) and acoordinate of the progressive refractive surface is taken as z_(t), arelationship of z_(t)=z_(p)+δ is established; and at the distanceportion along a main meridian line extending substantially in the Y-axisdirection of the progressive refractive surface, the δ is given byδ=g(r); at the near portion along the main meridian line extendingsubstantially in the Y-axis direction of the progressive refractivesurface, the d is given by δ=h(r); and at other portions, the δ is givenby δ=α·g(r)+β·h(r) where α and β satisfy the relationship of α+β=1.0,0≦α≦1, and 0≦β≦1; r is a distance from the progressively change startingpoint and is expressed by r=(x²+y²)^(½); and the g(r) and h(r) are eacha function depending only on r and satisfy the relationship of g(r)≠h(r) and g(0)=0.

According to a second invention, there is provided a progressive powerlens characterized in that at least one of two refractive surfacesforming a spectacle lens has a progressive refractive surface includinga distance portion and a near portion having different focal powers, anda progressive portion having a focal power progressively changed betweenthe distance and near portions; coordinates are defined such that,assuming that the progressive refractive surface of the lens assembledin each of spectacles is viewed from the front side of a user, thehorizontal direction is taken as an X-axis; the vertical direction(direction between the distance and near portions) is taken as a Y-axis;the depth direction is taken as a Z-axis; and a progressively changestarting point located at the lower end of the distance portion is takenas an origin (x, y, z)=(0, 0, 0); assuming that a radial inclination ofan original progressive refractive surface is taken as dz_(p) and aradial inclination of the progressive refractive surface is taken asdz_(t), a relationship of dz_(t)=dz_(p)+δ is established; and at thedistance portion along a main meridian line extending substantially inthe Y-axis direction of the progressive refractive surface, the δ isgiven by δ=g(r); at the near portion along the main meridian lineextending substantially in the Y-axis direction of the progressiverefractive surface, the δ is given by δ=h(r); and at other portions, theδ is given by δ=α·g(r)+β·h(r) where α and β satisfy the relationship ofα+β=1.0, 0≦α≦1, and 0≦β≦1; r is a distance from the progressively changestarting point and is expressed by r=(x²+y²)^(½); and the g(r) and h(r)are each a function depending only on r and satisfy the relationship ofg(r)≠h(r) and g(0)=0.

According to a third invention, there is provided a progressive powerlens characterized in that at least one of two refractive surfacesforming a spectacle lens has a progressive refractive surface includinga distance portion and a near portion having different focal powers, anda progressive portion having a focal power progressively changed betweenthe distance and near portions; coordinates are defined such that,assuming that the progressive refractive surface of the lens assembledin each of spectacles is viewed from the front side of a user, thehorizontal direction is taken as an X-axis; the vertical direction(direction between the distance and near portions) is taken as a Y-axis;the depth direction is taken as a Z-axis; and a progressively changestarting point located at the lower end of the distance portion is takenas an origin (x, y, z)=(0, 0, 0); assuming that a radial curvature of anoriginal progressive refractive surface is taken as c_(p) and a radialcurvature of the progressive refractive surface is taken as c_(t), arelationship of c_(t)=c_(p)+δ is established; and at the distanceportion along a main meridian line extending substantially in the Y-axisdirection of the progressive refractive surface, the δ is given byδ=g(r); at the near portion along the main meridian line extendingsubstantially in the Y-axis direction of the progressive refractivesurface, the δ is given by δ=h(r); and at other portions, the δ is givenby δ=α·g(r)+β·h(r) where α and β satisfy the relationship of α+β=1.0,0≦α1, and 0≦β≦1; r is a distance from the progressively change startingpoint and is expressed by r=(x²+y²)^(½); and the g(r) and h(r) are eacha function depending only on r and satisfy the relationship of g(r)≠h(r)and g(0)=0.

According to a fourth invention, there is provided a progressive powerlens characterized in that at least one of two refractive surfacesforming a spectacle lens has a progressive refractive surface includinga distance portion and a near portion having different focal powers, anda progressive portion having a focal power progressively changed betweenthe distance and near portions; coordinates are defined such that,assuming that the progressive refractive surface of the lens assembledin each of spectacles is viewed from the front side of a user, thehorizontal direction is taken as an X-axis; the vertical direction(direction between the distance and near portions) is taken as a Y-axis;the depth direction is taken as a Z-axis; and a progressively changestarting point located at the lower end of the distance portion is takenas an origin (x, y, z)=(0, 0, 0); assuming that a coordinate of anoriginal progressive refractive surface is taken as z_(p), and acoordinate of the progressive refractive surface is taken as z_(t), arelationship expressed by the following equation (2) using b_(p) definedby the following equation (1) is established; $\begin{matrix}{b_{p} = \frac{2z_{p}}{x^{2} + y^{2} + z_{p}^{2}}} & (1) \\{z_{t} = \frac{\left( {b_{p} + \delta} \right)r^{2}}{1 + \sqrt{1 - {\left( {b_{p} + \delta} \right)^{2}r^{2}}}}} & (2)\end{matrix}$

at the distance portion along a main meridian line extendingsubstantially in the Y-axis direction of the progressive refractivesurface, the δ is given by δ=g(r); at the near portion along the mainmeridian line extending substantially in the Y-axis direction of theprogressive refractive surface, the δ is given by δ=h(r); and at otherportions, the δ is given by δ=α·g(r)+β·h(r) where α and β satisfy therelationship of α+β=1.0, 0≦α≦1, and 0≦β≦1; r is a distance from theprogressively change starting point and is expressed by r=(X²+y²)^(½);and the g(r) and h(r) are each a function depending only on r andsatisfy the relationship of g(r)≠h(r) and g(0)=0.

According to a fifth invention, there is provided a progressive powerlens characterized in that at least one of two refractive surfacesforming a spectacle lens is configured as a progressive refractivesurface including a distance portion and a near portion having differentfocal powers, and a progressive portion in which a focal power isprogressively changed between the distance and near portions;coordinates are defined such that, assuming that the progressiverefractive surface of the lens assembled in each of spectacles is viewedfrom the front side of a user, the horizontal direction is taken as anX-axis; the vertical direction (direction between the distance and nearportions) is taken as a Y-axis; the depth direction is taken as aZ-axis; and a progressively change starting point located at the lowerend of the distance portion is taken as an origin (x, y, z)=(0, 0, 0);assuming that a coordinate of an original progressive refractive surfaceis taken as z_(p), and a coordinate of the progressive refractivesurface is taken as z_(t), a relationship expressed by the followingequation (3) using b_(p) defined by the following equation (1) isestablished; $\begin{matrix}{b_{p} = \frac{2z_{p}}{x^{2} + y^{2} + z_{p}^{2}}} & (1) \\{z_{t} = \frac{b_{p}r^{2}}{1 + \sqrt{1 - {\left( {1 + \delta} \right)b_{p}^{2}r^{2}}}}} & (3)\end{matrix}$

at the distance portion along a main meridian line extendingsubstantially in the Y-axis direction of the progressive refractivesurface, the δ is given by δ=g(r); at the near portion along the mainmeridian line extending substantially in the Y-axis direction of theprogressive refractive surface, the δ is given by δ=h(r); and at otherportions, the δ is given by δ=α·g(r)+β·h(r) where α and β satisfy therelationship of α+β1.0, 0≦α≦1, and 0≦β≦1; r is a distance from theprogressively change starting point and is expressed by r=(x²+y²)^(½);and the g(r) and h(r) are each a function depending only on r andsatisfy the relationship of g(r)≠h(r) and g(0)=0.

With respect to the above-described methods of calculating an additionalaspherical surface amount, the additional aspherical surface amount canbe smoothly given over the entire progressive refractive surface byinterpolating, in accordance with an angle at the progressively changestarting point, distributions of the ratio α of the optimum additionalaspherical surface amount g(r) at the distance portion and the ratio βof the optimum additional aspherical surface amount h(r) at the nearportion.

According to a sixth invention, there is provided a progressive powerlens according to any one of the first to fifth inventions, wherein anangle formed between a straight line extending from the progressivelychange starting point to the outer peripheral portion of the progressiverefractive surface and the X-axis is taken as w, the α and β satisfy thefollowing equations (4) and (5):

α=0.5+0.5 sin(w)  (4)

β=0.5−0.5 sin(w)  (5)

Upon determination of an additional aspherical surface amount byinterpolation, if an additional aspherical surface amount itself isinterpolated, the calculation becomes complicated because of a largeamount of data. To cope with such an inconvenience, there may be adopteda method in which functions each defining a distribution of additionalaspherical surface amount are prepared, and coefficients determining thefunctions are interpolated for each user's recipe. This is effective tosignificantly reduce the calculation amount, and hence to simplify thelens design.

According to a seventh invention, there is provided a progressive powerlens according to any one of the first to fifth inventions, wherein theg(r) and h(r) satisfy the following equations (6) and (7):$\begin{matrix}{{g(r)} = {\sum\limits_{n}{G_{n} \cdot \left( {r - r_{0}} \right)^{n}}}} & (6) \\{{h(r)} = {\sum\limits_{n}{H_{n} \cdot \left( {r - r_{0}} \right)^{n}}}} & (7)\end{matrix}$

where G_(n) and H_(n) are coefficients for determining g(r) and h(r),which are constants not depending on r for a certain progressiverefractive surface; and n is an integer of 2 or more.

Further, in consideration of a dioptric power measurement point by alensmeter, a circular portion having a specific radius r=r₀ centered atthe progressively change starting point may be preferably madeconfigured as a spherical design portion without addition of anyadditional aspherical surface amount. When r₀<r, the additionalaspherical surface amount may be preferably given by polynomialexpressions shown in the above-described equations (6) and (7). Thespecific distance r₀ may be preferably in a range capable of coveringthe dioptric power measurement point, concretely, in a range of 7 mm ormore and less than 12 mm.

According to an eighth invention, there is provided a progressive powerlens according to any of the first to fifth inventions, wherein when0≦r≦r₀, g(r) and h(r) satisfy the relationship of g(0)=0 and h(0)=0, andwhen r₀<r, g(r) and h(r) satisfy the following equations (6) and (7):$\begin{matrix}{{g(r)} = {\sum\limits_{n}{G_{n} \cdot \left( {r - r_{0}} \right)^{n}}}} & (6) \\{{h(r)} = {\sum\limits_{n}{H_{n} \cdot \left( {r - r_{0}} \right)^{n}}}} & (7)\end{matrix}$

where G_(n) and H_(n) are coefficients for determining g(r) and h(r),which are constants not depending on r for a certain progressiverefractive surface; and n is an integer of 2 or more.

According to a ninth invention, there is provided a progressive powerlens according to the eighth invention, wherein the r₀ is 7 mm or moreand less than 12 mm.

By providing the progressive refractive surface on the eye side, it ispossible to reduce the image jump and aberration which are drawbacks ofthe progressive power lens.

According to a tenth invention, there is provided a progressive powerlens according to any one of first to ninth inventions, wherein theprogressive refractive surface is provided on the eye side.

BRIEF DESCRIPTION OF DRAWINGS

FIGS. 1(a) and 1(b) show coordinates of a progressive power lens inwhich a progressive refractive surface is disposed on the outer surface,wherein FIG. 1(a) is a sectional view taken on surfaces along X-Z axespassing through a progressively change starting point, and FIG. 1(b) isa front view;

FIG. 2 is a front view of the progressive power lens of the presentinvention showing sections of a ratio between two kinds of additionalaspherical surface components added in the progressive refractivesurface;

FIG. 3 is a front view of the progressive power lens showing sections ofa ratio between two kinds of additional aspherical components added inthe progressive refractive surface;

FIG. 4 is a front view showing coordinates of the progressive refractivesurface of the progressive power lens of the present invention;

FIG. 5 is a front view showing a change in dioptric power along the mainmeridian line on the progressive refractive surface of the progressivepower lens and a dioptric power measurement point;

FIGS. 6(a) and 6(b) show coordinates of a progressive power lens inwhich a progressive refractive surface is arranged on the inner surface,wherein FIG. 6(a) is a sectional view taken on surfaces along X-Z axespassing through a progressively change starting point, and FIG. 6(b) isa front view;

FIG. 7 is a front view of a progressive power lens showing adistribution of astigmatism of a progressive power lens in which aprogressive refractive surface formed by spherical design is provided onthe eye side; and

FIG. 8 is a front view of the progressive power lens of the presentinvention showing a distribution of astigmatism of a progressive powerlens in which a progressive refractive surface formed by asphericaldesign is provided on the eye side.

BEST MODE FOR CARRYING OUT THE INVENTION

Hereinafter, embodiments of a progressive power lens according to thepresent invention will be described. The progressive power lens of thepresent invention used for correcting visual acuity includes tworefractive surfaces, on an object side and an eye side, forming aspectacle lens, wherein at least one of these refractive surfaces isconfigured as a progressive refractive surface having a distance portionand a near portion which are different in focal power from each other,and a progressive portion in which the focal power is progressivelychanged between the distance and near portions. The progressiverefractive surface is obtained by simply forming a new progressiverefractive shape by an aspherical design on the basis of a progressiverefractive shape formed by a spherical design, or simply forming, on thebasis of a progressive refractive shape formed by an aspherical designadapted for a certain user's recipe, a new progressive refractive shapeby an aspherical design optimum to another desired user's recipe.

According to the present invention, particularly, an additionalaspherical surface amount to be added to an aspherical progressive powerlens can be optimized for each user's recipe, and on the basis of theoptimum additional aspherical surface amount, the optimum progressiverefractive shape can be usually obtained by a simple calculating method.The method of the present invention, therefore, is suitable forproduction on order.

Referring to FIGS. 1(a) and 1(b), coordinates of a progressive powerlens are defined such that assuming that the progressive refractivesurface of the lens assembled in each of spectacles is viewed from thefront side of the user, the horizontal direction is taken as an X-axis;the vertical direction (direction between distance and near portions) istaken as a Y-axis; the depth direction is taken as a Z-axis; and aprogressively change starting point O located at the lower end of thedistance portion is taken as an origin, that is, (x, y, z)=(0, 0, 0).

According to the present invention, as described above, an additionalaspherical surface amount for each user's recipe is not determined onthe basis of ray tracing but is determined by a method wherein theoptimum additional aspherical surface amount is previously determined byactual ray tracing for several examples selected from a range of user'srecipes using a common basic progressive refractive surface, and then anew additional aspherical surface amount for a desired user's recipe isdetermined by interpolation using a function defining a distribution ofadditional aspherical surface amounts prepared on the basis of theoptimum additional aspherical surface amount. The additional asphericalsurface amount is calculated in accordance with the following fivecalculating methods:

The first method of calculating an additional aspherical surface amountis to directly calculate the coordinate of the additional asphericalsurface amount in the z-axis direction. An original coordinate Z_(p) ofa progressive refractive surface in the depth direction is expressed bya function of coordinates (x, y) as follows:

Z_(p)=f (x, y)

When an additional aspherical surface amount δ in the z-axis directionis added to z_(p), assuming that a synthesized coordinate in the z-axisdirection after addition of δ, that is, a coordinate of a newprogressive refractive surface is taken as z_(t), the coordinate z_(t)is expressed by

z_(t)=Z_(p)+δ

At this time, an additional aspherical surface amount added to a portionin the vicinity of the optical axis of the lens (in the vicinity of theprogressively change starting point O) may be small because prism issmall and astigmatism less occurs at such a portion; however, sincelight rays are made obliquely incident on a lens outer peripheralportion, astigmatism easily occurs thereat, and thereby an additionalaspherical surface amount added to such a portion for correcting theastigmatism generally becomes large. The ideal additional asphericalsurface amount actually added, which differs depending on the user'srecipe (dioptric power of a lens), is changed in accordance with adistance r from the optical axis (progressively change starting pointO). Consequently, the optimum additional aspherical surface amount δbecomes a function of the distance r=(x²+y²)^(½) from the progressivelychange starting point O.

Since the focal power of the progressive power lens differs between thedistance and near portions, the optimum additional aspherical surfaceamount may be desirable to differ between the distance and nearportions. Consequently, the additional coordinate δ at the distanceportion and the near portion along the main meridian line extendingsubstantially in the Y-axis direction of the progressive refractivesurface satisfies the following conditions:

δ=g(r)

δ=h(r)

δg(r)≠h(r)

where g(0)=0 at the progressively change starting point O, and each ofg(r) and h(r) is a function depending only on r.

In the progressive power lens of the present invention, the large orsmall relationship between the optimum additional aspherical surfaceamount g(r) at the distance portion and the optimum additionalaspherical surface amount h(r) at the near portion differs depending onthe recipe of the lens, and therefore, it is not specified. However,since within one progressive power lens, the dioptric power of the lensis generally in a range of the dioptric power for distance and thedioptric power for near vision, the additional aspherical component δmay be set in a range of g(r) and h(r). In this case, according to thepresent invention, a ratio between g(r) and h(r) is determined inaccordance with a desired distance set for each portion of theprogressive power lens. For example, at the distance portion, δ isdetermined by 100% of g(r) and 0% of h(r); at the near portion, δ isdetermined by 0% of g(r) and 100% of h(r); and at the progressiveportion, δ is progressively changed from g(r) to h(r) for obtaining anoptically continuous refractive shape. Accordingly, a portion at which δis determined by 50% of g(r) and 50% of h(r) is present between thedistance portion and the near portion.

Consequently, at a portion other than the distance and near portionsalong the meridian line extending substantially in the Y-axis directionof the progressive refractive surface of the progressive power lens, theadditional aspherical surface amount δ has the following relationship:

δ=α·g(r)+β·h(r)

α+β=1.0

0≦α≦1

0≦β≦1

By setting the values of α and β in accordance with a desired distanceset for each arbitrary point of the progressive power lens, an idealaspherical shape can be easily added to the original progressiverefractive surface.

The first method of calculating an additional aspherical surface amountis advantageous in that since the coordinates can be directlydetermined, calculation can be easily performed.

The second method of calculating an additional aspherical surface amountis characterized in that assuming that a radial inclination of anoriginal progressive refractive surface is taken as dz_(p) and aninclination of a new progressive refractive surface is taken as dz_(t),the relationship of dz_(t) =dz_(p)+δ is established. Like the firstcalculating method, an additional aspherical surface amount δ is δ=g(r)at the distance portion along the main meridian line extendingsubstantially in the Y-axis direction of the progressive refractivesurface; δ=h(r) at the near portion along the main meridian lineextending substantially in the Y-axis direction of the progressiverefractive surface; and δ=α·g(r)+β·h(r) at other portions.

In the above equations, α and β satisfy the relationship of α+β=1.0,0≦α≦1, and 0≦β≦1; r is a distance from the progressively change startingpoint O and is expressed by r=(x²+y²)^(½); and g(r) and h(r) are each afunction depending only on r and satisfy the relationship of g(r)≠h(r)and g(0)=0.

The second method of calculating an additional aspherical surfaceamount, in which an additional aspherical surface amount is calculatedon the basis of a distribution of inclinations, is advantageous in thatthe control of a prism amount can be easily performed. The Z-coordinatecan be determined by integration based on the origin.

The third method of calculating an additional aspherical surface amountis characterized in that assuming that a radial curvature of an originalprogressive refractive surface is taken as c_(p) and a curvature of anew progressive refractive surface is taken as c_(t), the relationshipof c_(t)=c_(p)+δ is established. An additional aspherical surface amountδ is δ=g(r) at the distance portion along the main meridian lineextending substantially in the Y-axis direction of the progressiverefractive surface; δ=h(r) at the near portion along the main meridianline extending substantially in the Y-axis direction of the progressiverefractive surface; and δ=α·g(r)+β·h(r) at other portions.

In the above equations, a and B satisfy the relationship of α+β=1.0,0≦α≦1, and 0≦β≦1; r is a distance from the progressively change startingpoint O and is expressed by r=(x²+y²)^(½); and g(r) and h(r) are each afunction depending only on r and satisfy the relationship of g(r)≠h(r)and g(0)=0.

The third method of calculating an additional aspherical surface amount,in which an additional aspherical surface amount is calculated on thebasis of a distribution of curvatures, is advantageous in that theoptical evaluation is simplified and the aspherical design isfacilitated, to easily form an aspherical shape in accordance with adesired user's recipe. The Z-coordinate can be determined by integrationbased on the origin.

The fourth method of calculating an additional aspherical surface amountis characterized in that assuming that a coordinate of an originalprogressive refractive surface is taken as z_(p); a coordinate of a newprogressive refractive surface is taken as z_(t); and a factor forconverting a Z-coordinate of a progressive refractive surface into acurvature is defined as b_(p) expressed the following equation (1), therelationship expressed by the following equation (2) is established.$\begin{matrix}{b_{p} = \frac{2z_{p}}{x^{2} + y^{2} + z_{p}^{2}}} & (1) \\{z_{t} = \frac{\left( {b_{p} + \delta} \right)r^{2}}{1 + \sqrt{1 - {\left( {b_{p} + \delta} \right)^{2}r^{2}}}}} & (2)\end{matrix}$

An additional aspherical surface amount δ is δ=g(r) at the distanceportion along the main meridian line extending substantially in theY-axis direction of the progressive refractive surface; δ=h(r) at thenear portion along the main meridian line extending substantially in theY-axis direction of the progressive refractive surface; andδ=α·g(r)+β·h(r) at other portions.

In the above equations, α and β satisfy the relationship of α+β=1.0,0≦α≦1, and 0≦β≦1; r is a distance from the progressively change startingpoint O and is expressed by r=(x²+y²)^(½); and g(r) and h(r) are each afunction depending only on r and satisfy the relationship of g(r)≠h(r)and g(0)=0.

The fourth method of calculating an additional aspherical surfaceamount, in which an additional aspherical surface amount is calculatedon the basis of a distribution of curvatures, is advantageous in thatthe optical evaluation is simplified and the aspherical design isfacilitated, to easily form an aspherical shape in accordance with adesired user's recipe, and further the Z-coordinate can be directlycalculated without use of integration.

The fifth method of calculating an additional aspherical surface amountis characterized in that assuming that a coordinate of an originalprogressive refractive surface is taken as z_(p); a coordinate of a newprogressive refractive surface is taken as z_(t); and a factor forconverting a Z-coordinate of a progressive refractive surface into acurvature is defined as b_(p) expressed the following equation (1), therelationship expressed by the following equation (3) is established.$\begin{matrix}{b_{p} = \frac{2z_{p}}{x^{2} + y^{2} + z_{p}^{2}}} & (1) \\{z_{t} = \frac{b_{p}r^{2}}{1 + \sqrt{1 - {\left( {1 + \delta} \right)b_{p}^{2}r^{2}}}}} & (3)\end{matrix}$

An additional aspherical surface amount δ is δ=g(r) at the distanceportion along the main meridian line extending substantially in theY-axis direction of the progressive refractive surface; δ=h(r) at thenear portion along the main meridian line extending substantially in theY-axis direction of the progressive refractive surface; andδ=α·g(r)+β·h(r) at other portions.

In the above equations, α and β satisfy the relationship of α+β=1.0,0≦α≦1, and 0≦β≦1; r is a distance from the progressively change startingpoint O and is expressed by r=(x²+y²)^(½); and g(r) and h(r) are each afunction depending only on r and satisfy the relationship of g(r)≠h(r)and g(0)=0.

The fifth method of calculating an additional aspherical surface amountis advantageous in that the design can be performed in such a manner asto make smooth the change in curvature, to form a natural progressiverefractive shape without rapid change in dioptric power.

The value α expressing the ratio of the optimum additional asphericalsurface amount g(r) which is the additional aspherical surface amount δat the distance portion, and the value β expressing the ratio of theoptimum additional aspherical surface amount h(r) which is theadditional aspherical surface amount δ at the near portion areinterpolated as follows:

For example, as shown in FIG. 2, an original progressive refractivesurface partitioned by straight lines into a distance portion, aprogressive portion, and a near portion in such a manner that at thedistance portion at which the ratio of g(r) is 100%, α:β=100:0 is given;at the near portion, α:β=0:100 is given; and at the progressive portionat which the focal power is changed, α:β is progressively changed inaccordance with a desired distance.

As shown in FIG. 3, an original progressive refractive surface is oftenpartitioned by sectors substantially centered at the progressivelychange starting point O located at the lower end of the distanceportion. In such a case, by determining the value of the additionalaspherical far-vision/near-vision ratio α:β in accordance with thesector partition of the original progressive refractive surface, it ispossible to effectively improve the optical performance and toeffectively thin the lens.

As shown in FIG. 4, assuming that an angle formed between a straightline OQ extending from the progressively change starting point O to theouter peripheral portion of a progressive refractive surface and theX-axis is taken as w, the values of α and β may be set to satisfy thefollowing equations (4) and (5).

α=0.5+0.5 sin(w)  (4)

β=0.5−0.5 sin(w)  (5)

By use of the values α and β thus set, a smooth additional asphericalsurface component can be added to the entire area of the progressiverefractive surface.

For example, as a result of calculating an additional aspherical surfacecomponent to be added to the distance portion along the main meridianline on the basis of the above equations, since w=90°, α=1 and β=0°,that is, only the additional aspherical surface component for distance(α) of 100% is given. For a portion along in the horizontal direction ofthe progressive power lens, since w=0 or w=180°, α=β0.5, that is, theadditional aspherical surface component for distance (α) of 50% and theadditional aspherical surface component for near vision (β) of 50% aregiven. Further, a change in additional aspherical surface component issmoothly shifted over the entire area of the progressive refractivesurface.

The optimum additional aspherical surface amount g(r) at the distanceportion and the optimum additional aspherical surface amount h(r) at thenear portion may preferably satisfy the following equations (6) and (7)given as polynomial expressions of r: $\begin{matrix}{{g(r)} = {\sum\limits_{n}{G_{n} \cdot \left( {r - r_{0}} \right)^{n}}}} & (6) \\{{h(r)} = {\sum\limits_{n}{H_{n} \cdot \left( {r - r_{0}} \right)^{n}}}} & (7)\end{matrix}$

In the above equations, G_(n) and H_(n) are coefficients for determiningg(r) and h(r), which are constants not depending on r for a certainprogressive refractive surface; and n is an integer of 2 or more.

Upon determination of an additional aspherical surface amount byinterpolation, if an additional aspherical surface amount itself isinterpolated, the calculation becomes complicated because of a largeamount of data. To cope with such an inconvenience, there may be adopteda method in which the above functions g(r) and h(r) defining adistribution of additional aspherical surface amount are expressed bythe above equations (6) and (7), and the coefficients G_(n) and H_(n)determining the functions are interpolated with respect to the same termn for each user's recipe. This is effective to significantly reduce thecalculation amount, and hence to simplify the lens design.

Next, a progressive power lens produced in consideration of the dioptricpower measured by using a lensmeter will be described. The dioptricpower added to the progressive power lens is, as shown in FIG. 5,progressively changed from the progressively change starting point O.Accordingly, upon measurement of the dioptric power by the lensmeter, adioptric power measurement point is generally set at a position offset5-10 mm on the distance portion side from the progressively changestarting point O in consideration of the width of a light ray emittedfrom the lensmeter. However, if the aspherical design is applied up tothe vicinity of the progressively change starting point O, when thedioptric power is measured by the lensmeter, the dioptric power of thelens cannot be guaranteed because of occurrence of astigmatism.

To cope with such an inconvenience, as shown in FIG. 5, a circularportion having a specific radius r=r₀ centered at the progressivelychange starting point O may be preferably made configured as a sphericaldesign portion without addition of any additional aspherical surfaceamount. To be more specific, when 0≦r≦r₀, the relationship of g(0)=0 andh(0)=0, that is, δ=0 may be given, and when r₀<r, g(r) and h(r) maysatisfy the above-described equations (6) and (7). The specific distancer₀ may be preferably in a range capable of covering the dioptric powermeasurement point, concretely, in a range of 7 mm or more and less than12 mm.

The provision of such a spherical design portion does not particularlyexert an effect to the optical performance because the vicinity of theprogressively change starting point O is near the optical axis, andtherefore, an ideal additional aspherical surface amount to be addedthereto is essentially small.

While the several embodiments of the progressive power lens of thepresent invention have been described, the most suitable form of theprogressive power lens of the present invention can be obtained byarranging the progressive refractive surface on the inner surface side,that is, on the refractive surface on the eye side.

By arranging the progressive refractive surface on the inner surface,the refractive surface on the outer surface side can be configured as aspherical surface. It is known that such a configuration is able toreduce the image jump and aberration which are drawbacks of theprogressive power lens and hence to improve the optical performance(W097/19382). If the present invention is applied to the progressivepower lens in which the progressive refractive surface is arranged onthe inner surface, there can be realized, in addition to the effect ofreducing the image jump and aberration disclosed in W097/19382, theeffects of the present invention, that is, the reduction in astigmatismand thinning of the lens.

To apply the present invention to the progressive refractive surfacedisclosed in W097/19382, the coordinates shown in FIGS. 1(a) and 1(b)may be converted into those shown in FIGS. 6(a) and 6(b).

Further, to keep up with an astigmatic user's recipe, an asphericalsurface may be added to a free curve surface obtained by synthesizing aprogressive refractive surface and an astigmatic surface, which isdisclosed in W097/19382, in accordance with the above-described method.

To be more specific, a coordinate z at an arbitrary point P (x, y, z) ona surface on the eye side is expressed by the following equation (8) byusing an approximate curvature Cp at the arbitrary point P on aprogressive refractive surface formed by spherical design, andcurvatures Cx and Cy in the x and y directions on a toric surface addedto the progressive refractive surface formed by spherical design.$\begin{matrix}{z = \frac{{\left( {{Cp} + {Cx}} \right)x^{2}} + {\left( {{Cp} + {Cy}} \right)y^{2}}}{1 + \sqrt{1 - {\left( {{Cp} + {Cx}} \right)^{2}x^{2}} - {\left( {{Cp} + {Cy}} \right)^{2}y^{2}}}}} & (8)\end{matrix}$

In accordance with the method of the present invention, an additionalaspherical surface amount may be added to a free curve surface obtainedby synthesizing the progressive refractive surface calculated and anastigmatic surface by using the equation (8). In this case, it may bedesirable to use the above-described fourth method of calculating anadditional aspherical surface amount.

The application of the present invention to a progressive power lens inwhich the progressive refractive surface is arranged on the innersurface has further merit. In the case of a progressive power lens inwhich the progressive refractive surface is arranged on the outersurface, the addition power is guaranteed on the outer side, and thespherical power and astigmatic power are ensured by polishing the innersurface side at a specific curvature. Accordingly, although the innersurface side is formed into a shape which differs for each user, theprogressive refractive surface on the outer side is formed into a shapewhich is made constant for each user insofar as the user's dioptricpower is in a specific dioptric power range. As a result, the optimumaspherical surface cannot be added to the progressive refractive surfacefor each dioptric power. In other words, the constant aspherical surfacemust be added for the unsuitable dioptric power.

For a progressive power lens in which the progressive refractive surfaceis arranged on the inner surface, however, the spherical power,astigmatic power, and addition power, which differ for each user, can bedetermined only by setting the shape of the inner surface. The designfor such a progressive power lens thus becomes a perfect custom-madedesign. As a result, an additional aspherical surface amount suitablefor a predetermined recipe including the dioptric power can be added tothe inner surface of the lens.

Examples of the present invention will be described below. FIG. 7 showsa distribution of astigmatism of a spectacle lens produced by sphericaldesign in which a progressive refractive surface is formed on the eyeside in accordance with the recipe of S=+4.0 D, C=0 D, and the additionpower is 2.0 D. FIG. 8 shows a distribution of astigmatism of a lens byaspherical design, modified from the lens shown in FIG. 7, in which anadditional aspherical surface amount is added to the inner surfaceprogressive lens in accordance with the present invention. As isapparent from these figures, the astigmatism is improved and thereby theoptical performance is enhanced by the method of the present invention.

First Example

To obtain the inner surface progressive lens by aspherical design shownin FIG. 8, an additional aspherical surface amount is calculated inaccordance with the first method of calculating an additional asphericalsurface amount. In this case, g(r) and h(r) in the first calculatingmethod are expressed by the polynomial expressions of r on the basis ofthe equations (6) and (7). Respective parameters of the equations (6)and (7) in this case are shown in Table 1. The radius r₀ of thespherical design portion is set at 10 mm.

TABLE 1 Parameter Value r₀ 10 G₄  2.45E-06 G₆ −5.94E-09 G₈  5.23E-12 H₄ 1.52E-06 H₆ −4.18E-09 H₈  5.31E-12

By using the parameters shown in Table 1, the change in additionalaspherical surface amount δ (unit: μm) is calculated depending on thevalues α and β expressed by the equations (4) and (5) as the functionsof the angle w centered at the progressively change starting point O,and on the distance r from the progressively change starting point O andon the angle w centered at the progressively change starting point O.The result is shown in Table 2.

TABLE 2 r\w 0 30 60 90 120 150 180 210 240 270 300 330 360 α 0.500 0.7500.933 1.000 0.933 0.750 0.500 0.250 0.067 0.000 0.067 0.250 0.500 β0.500 0.250 0.067 0.000 0.067 0.250 0.500 0.750 0.933 1.000 0.933 0.7500.500 10 0 0 0 0 0 0 0 0 0 0 0 0 0 11 0 0 0 0 0 0 0 0 0 0 0 0 0 12 0 0 00 0 0 0 0 0 0 0 0 0 13 0 0 0 0 0 0 0 0 0 0 0 0 0 14 0 1 1 1 1 1 0 0 0 00 0 0 16 2 3 3 3 3 3 2 2 2 2 2 2 2 17 4 5 5 5 5 5 4 4 3 3 3 4 4 18 7 8 89 8 8 7 6 5 5 5 6 7 19 11 12 13 13 13 12 11 9 8 8 8 9 11 20 15 17 19 1919 17 15 13 12 12 12 13 15 21 21 24 26 26 26 24 21 19 17 16 17 19 21 2228 32 34 35 34 32 28 25 22 21 22 25 28 23 37 41 44 46 44 41 37 32 29 2829 32 37 24 46 52 56 57 56 52 46 40 36 35 36 40 46 25 56 63 68 70 68 6356 50 45 43 45 50 56 26 68 76 81 83 81 76 68 60 54 52 54 60 68 27 80 8995 98 95 89 80 72 65 63 65 72 80 28 94 104 110 113 110 104 94 85 78 7678 85 94 29 110 119 126 129 126 119 110 101 94 92 94 101 110 30 129 137143 146 143 137 129 120 114 112 114 120 129

Second Example

To obtain the inner surface progressive lens shown in FIG. 8, anadditional aspherical surface amount is calculated in accordance withthe second method of calculating an additional aspherical surfaceamount. In this case, g(r) and h(r) in the second calculating method areexpressed by the polynomial expressions of r on the basis of theequations (6) and (7). Respective parameters of the equations (6) and(7) in this case are shown in table 3. The radius r₀ of the sphericaldesign portion is set at 10 mm.

TABLE 3 Parameter Value r₀ 10 G₃  9.80E-06 G₅ −3.56E-08 G₇  4.22E-11 H₃ 6.10E-06 H₅ −2.51E-08 H₇  4.25E-11

By using the parameters shown in Table 3, the change in additionalaspherical surface amount δ (actual value multiplied by 10000) iscalculated depending on the values α and β expressed by the equations(4) and (5) as the functions of the angle w centered at theprogressively change starting point O, and on the distance r from theprogressively change starting point O and on the angle w centered at theprogressively change starting point O. The result is shown in Table 4.

TABLE 4 r\w 0 30 60 90 120 150 180 210 240 270 300 330 360 α 0.500 0.7500.933 1.000 0.933 0.750 0.500 0.250 0.067 0.000 0.067 0.250 0.500 β0.500 0.250 0.067 0.000 0.067 0.250 0.500 0.750 0.933 1.000 0.933 0.7500.500 10 0 0 0 0 0 0 0 0 0 0 0 0 0 11 0 0 0 0 0 0 0 0 0 0 0 0 0 12 1 1 11 1 1 1 1 0 0 0 1 1 13 2 2 2 3 2 2 2 2 2 2 2 2 2 14 5 5 6 6 6 5 5 4 4 44 4 5 15 9 10 11 11 11 10 9 8 7 7 7 8 9 16 15 17 18 19 18 17 15 13 12 1112 13 15 17 23 25 27 28 27 25 23 20 18 17 18 20 23 18 32 36 38 39 38 3632 28 25 24 25 28 32 19 42 47 51 52 51 47 42 37 33 32 33 37 42 20 53 6065 67 65 60 53 47 42 40 42 47 53 21 65 73 79 81 79 73 65 57 51 49 51 5765 22 77 86 93 96 93 86 77 68 61 58 61 68 77 23 89 99 107 110 107 99 8978 70 67 70 78 89 24 100 111 119 122 119 111 100 88 80 77 80 88 100 25110 121 130 133 130 121 110 99 91 88 91 99 110 26 121 131 139 141 139131 121 111 103 101 103 111 121 27 133 141 147 149 147 141 133 126 120118 120 126 133 28 149 153 156 157 156 153 149 146 143 142 143 146 14929 172 170 169 168 169 170 172 175 176 177 176 175 172 30 207 196 188185 188 196 207 218 226 229 226 218 207

Third Example

To obtain the inner surface progressive lens shown in FIG. 8, anadditional aspherical surface amount is calculated in accordance withthe third method of calculating an additional aspherical surface amount.In this case, g(r) and h(r) in the third calculating method areexpressed by the polynomial expressions of r on the basis of theequations (6) and (7). Respective parameters of the equations (6) and(7) in this case are shown in Table 5. The radius r₀ of the sphericaldesign portion is set at 10 mm.

TABLE 5 Parameter Value r₀ 10 G₂  2.83E-05 G₄ −7.60E-08 G₆  8.20E-11 H₂ 1.85E-05 H₄ −4.82E-08 H₆  6.43E-11

By using the parameters shown in Table 5, the change in additionalaspherical surface amount δ (actual value multiplied by 100000) iscalculated depending on the values α and β expressed by the equations(4) and (5) as the functions of the angle w centered at theprogressively change starting point O, and on the distance r from theprogressively change starting point O and on the angle w centered at theprogressively change starting point O. The result is shown in Table 6.

TABLE 6 r\w 0 30 60 90 120 150 180 210 240 270 300 330 360 α 0.500 0.7500.933 1.000 0.933 0.750 0.500 0.250 0.067 0.000 0.067 0.250 0.500 β0.500 0.250 0.067 0.000 0.067 0.250 0.500 0.750 0.933 1.000 0.933 0.7500.500 10 0 0 0 0 0 0 0 0 0 0 0 0 0 11 2 3 3 3 3 3 2 2 2 2 2 2 2 12 9 1011 11 11 10 9 8 8 7 8 8 9 13 21 23 24 25 24 23 21 18 17 16 17 18 21 1436 40 42 43 42 40 36 32 29 28 29 32 36 15 55 60 65 66 65 60 55 49 45 4345 49 55 16 77 84 90 92 90 84 77 69 63 61 63 69 77 17 101 111 119 121119 111 101 90 83 80 83 90 101 18 126 139 149 152 149 139 126 113 104100 104 113 126 19 153 168 180 184 180 168 153 137 126 122 126 137 15320 179 197 210 215 210 197 179 161 148 143 148 161 179 21 205 225 240246 240 225 205 185 170 165 170 185 205 22 230 252 268 274 268 252 230208 192 186 192 208 230 23 253 277 294 301 294 277 253 230 212 206 212230 253 24 275 300 318 324 318 300 275 251 232 226 232 251 275 25 295320 339 345 339 320 295 270 252 245 252 270 295 26 315 339 357 364 357339 315 290 272 266 272 290 315 27 334 358 375 381 375 358 334 311 294287 294 311 334 28 355 377 392 398 392 377 355 334 318 312 318 334 35529 380 398 412 417 412 398 380 361 347 342 347 361 380 30 411 426 437441 437 426 411 395 384 380 384 395 411

Fourth Example

To obtain the inner surface progressive lens shown in FIG. 8, anadditional aspherical surface amount is calculated in accordance withthe fourth method of calculating an additional aspherical surfaceamount. In this case, g(r) and h(r) in the fourth calculating method areexpressed by the polynomial expressions of r on the basis of theequations (6) and (7). Respective parameters of the equations (6) and(7) in this case are shown in Table 7. The radius r₀ of the sphericaldesign portion is set at 10 mm.

TABLE 7 Parameter Value r₀ 10 G₂  2.31E-05 G₄ −5.00E-08 G₆  4.35E-11 H₂ 1.63E-05 H₄ −4.24E-08 H₆  5.41E-11

By using the parameters shown in Table 7, the change in additionalaspherical surface amount δ (actual value multiplied by 100000) O iscalculated depending on the values α and β expressed by the equations(4) and (5) as the functions of the angle w centered at theprogressively change starting point O, and on the distance r from theprogressively change starting point O and on the angle w centered at theprogressively change starting point. The result is shown in Table 8.

TABLE 8 r\w 0 30 60 90 120 150 180 210 240 270 300 330 360 α 0.500 0.7500.933 1.000 0.933 0.750 0.500 0.250 0.067 0.000 0.067 0.250 0.500 β0.500 0.250 0.067 0.000 0.067 0.250 0.500 0.750 0.933 1.000 0.933 0.7500.500 10 0 0 0 0 0 0 0 0 0 0 0 0 0 11 2 2 2 2 2 2 2 2 2 2 2 2 2 12 8 8 99 9 8 8 7 7 6 7 7 8 13 17 19 20 20 20 19 17 16 15 14 15 16 17 14 30 3335 36 35 33 30 28 26 25 26 28 30 15 46 51 54 55 54 51 46 42 39 38 39 4246 16 65 71 75 77 75 71 65 59 55 53 55 59 65 17 86 94 100 102 100 94 8678 72 70 72 78 86 18 108 118 126 129 126 118 108 98 91 88 91 98 108 19132 144 153 157 153 144 132 119 110 107 110 119 132 20 156 171 181 185181 171 156 141 130 126 130 141 156 21 179 197 209 214 209 197 179 162149 145 149 162 179 22 202 222 237 242 237 222 202 183 168 163 168 183202 23 225 247 263 269 263 247 225 203 186 180 186 203 225 24 245 269287 293 287 269 245 221 204 197 204 221 245 25 265 291 309 316 309 291265 239 221 214 221 239 265 26 283 310 330 337 330 310 283 257 237 230237 257 283 27 301 328 348 355 348 328 301 274 255 248 255 274 301 28319 345 365 372 365 345 319 293 274 267 274 293 319 29 339 363 380 387380 363 339 315 297 290 297 315 339 30 361 382 397 402 397 382 361 340325 320 325 340 361

Fifth Example

To obtain the inner surface progressive lens shown in FIG. 8, anadditional aspherical surface amount is calculated in accordance withthe fifth method of calculating an additional aspherical surface amount.In this case, g(r) and h(r) in the fifth calculating method areexpressed by the polynomial expressions of r on the basis of theequations (6) and (7). Respective parameters of the equations (6) and(7) in this case are shown in Table 9. The radius r₀ of the sphericaldesign portion is set at 10 mm.

TABLE 9 Parameter Value r₀ 10 G₁  0.783 G₃ −5.30E-04 H₁  0.485 H₃ 5.34E-04

By using the parameters shown in Table 9, the change in additionalaspherical surface amount δ (actual value) is calculated depending onthe values α and β expressed by the equations (4) and (5) as thefunctions of the angle w centered at the progressively change startingpoint O, and on the distance r from the progressively change startingpoint O and on the angle w centered at the progressively change startingpoint O. The result is shown in Table 10.

TABLE 10 r\w 0 30 60 90 120 150 180 210 240 270 300 330 360 α 0.5000.750 0.933 1.000 0.933 0.750 0.500 0.250 0.067 0.000 0.067 0.250 0.500β 0.500 0.250 0.067 0.000 0.067 0.250 0.500 0.750 0.933 1.000 0.9330.750 0.500 10 0.00 0.00 0.00 000 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 11 0.63 0.71 0.76 0.78 0.76 0.71 0.63 0.56 0.51 0.49 0.51 0.560.63 12 1.27 1.41 1.52 1.56 1.52 1.41 1.27 1.12 1.01 0.97 1.01 1.12 1.2713 1.90 2.12 2.28 2.33 2.28 2.12 1.90 1.69 1.53 1.47 1.53 1.69 1.90 142.54 2.82 3.02 3.10 3.02 2.82 2.54 2.26 2.05 1.97 2.05 2.26 2.54 15 3.173.51 3.76 3.85 3.76 3.51 3.17 2.83 2.58 2.49 2.58 2.83 3.17 16 3.80 4.194.48 4.58 4.48 4.19 3.80 3.41 3.13 3.03 3.13 3.41 3.80 17 4.44 4.87 5.185.30 5.18 4.87 4.44 4.01 3.69 3.58 3.69 4.01 4.44 18 5.07 5.53 5.87 5.995.87 5.53 5.07 4.61 4.28 4.15 4.28 4.61 5.07 19 5.71 6.18 6.53 6.66 6.536.18 5.71 5.23 4.88 4.75 4.88 5.23 5.71 20 6.34 6.82 7.17 7.30 7.17 6.826.34 5.86 5.51 5.38 5.51 5.86 6.34 21 6.98 7.44 7.78 7.91 7.78 7.44 6.986.51 6.17 6.05 6.17 6.51 6.98 22 7.61 8.05 8.36 8.48 8.36 8.05 7.61 7.186.86 6.74 6.86 7.18 7.61 23 8.25 8.63 8.91 9.01 8.91 8.63 8.25 7.86 7.587.48 7.58 7.86 8.25 24 8.88 9.19 9.42 9.51 9.42 9.19 8.88 8.57 8.34 8.268.34 8.57 8.88 25 9.52 9.74 9.90 9.96 9.90 9.74 9.52 9.30 9.14 9.08 9.149.30 9.52 26 10.15 10.25 10.33 10.36 10.33 10.25 10.15 10.05 9.97 9.959.97 10.05 10.15 27 10.79 10.75 10.72 10.71 10.72 10.75 10.79 10.8310.86 10.87 10.86 10.83 10.79 28 11.42 11.21 11.06 11.00 11.06 11.2111.42 11.63 11.79 11.84 11.79 11.63 11.42 29 12.06 11.65 11.35 11.2411.35 11.65 12.06 12.47 12.77 12.88 12.77 12.47 12.06 30 12.70 12.0611.59 11.42 11.59 12.06 12.70 13.33 13.80 13.97 13.80 13.33 12.70

According to the progressive power lens of the present invention, theoptimum aspherical component can be added over the entire area of thelens on the basis of a simple design, to realize improvement of theoptical performance such as reduction in astigmatism and thinning of thelens.

INDUSTRIAL APPLICABILITY

The progressive power lens of the present invention is usable as aspectacle lens for correcting visual acuity, which includes a distanceportion, a near portion, and a progressive portion therebetween.

What is claimed is:
 1. A progressive power lens characterized in that atleast one of two refractive surfaces forming a spectacle lens has aprogressive refractive surface including a distance portion and a nearportion having different focal powers, and a progressive portion havinga focal power progressively changed between said distance and nearportions; coordinates are defined such that, assuming that saidprogressive refractive surface of the lens assembled in each ofspectacles is viewed from the front side of a user, the horizontaldirection is taken as an X-axis; the vertical direction (directionbetween said distance and near portions) is taken as a Y-axis; the depthdirection is taken as a Z-axis; and a progressively change startingpoint located at the lower end of said distance portion is taken as anorigin (x, y, z)=(0, 0, 0); assuming that a coordinate of an originalprogressive refractive surface is taken as z_(p) and a coordinate ofsaid progressive refractive surface is taken as z_(t), a relationship ofz_(t)=z_(p)+δ is established; and at said distance portion along a mainmeridian line extending substantially in the Y-axis direction of saidprogressive refractive surface, said δ is given by δ=g(r); at said nearportion along the main meridian line extending substantially in theY-axis direction of said progressive refractive surface, said δ is givenby δ=h(r); and at other portions, said δ is given by δ=α·g(r)+β·h(r)where α and β satisfy the relationship of α+β=1.0, 0≦α≦1, and 0≦β≦1; ris a distance from said progressively change starting point and isexpressed by r=(x²+y²)^(½); and said g(r) and h(r) are each a functiondepending only on r and satisfy the relationship of g(r)≠h(r) andg(0)=0.
 2. A progressive power lens according to claim 1, wherein anangle formed between a straight line extending from the progressivelychange starting point to the outer peripheral portion of saidprogressive refractive surface and said X-axis is taken as w, said α andβ satisfy the following equations (4) and (5): α=0.5+0.5 sin(w)  (4)β=0.5−0.5 sin(w)  (5).
 3. A progressive power lens according to claim 1,wherein said g(r) and h(r) satisfy the following equations (6) and (7):$\begin{matrix}{{g(r)} = {\sum\limits_{n}{G_{n} \cdot \left( {r - r_{0}} \right)^{n}}}} & (6) \\{{h(r)} = {\sum\limits_{n}{H_{n} \cdot \left( {r - r_{0}} \right)^{n}}}} & (7)\end{matrix}$

where G_(n) and H_(n) are coefficients for determining g(r) and h(r),which are constants not depending on r for a certain progressiverefractive surface; and n is an integer of 2 or more.
 4. A progressivepower lens according to claim 1, wherein when 0≦r≦r₀, g(r) and h(r)satisfy the relationship of g(0)=0 and h(0)=0, and when r₀<r, g(r) andh(r) satisfy the following equations (6) and (7): $\begin{matrix}{{g(r)} = {\sum\limits_{n}{G_{n} \cdot \left( {r - r_{0}} \right)^{n}}}} & (6) \\{{h(r)} = {\sum\limits_{n}{H_{n} \cdot \left( {r - r_{0}} \right)^{n}}}} & (7)\end{matrix}$

where G_(n) and H_(n) are coefficients for determining g(r) and h(r),which are constants not depending on r for a certain progressiverefractive surface; and n is an integer of 2 or more.
 5. A progressivepower lens according to claim 4, wherein said r₀ is 7 mm or more andless than 12 mm.
 6. A progressive power lens according to claim 1,wherein said progressive refractive surface is provided on the eye side.7. A progressive power lens characterized in that at least one of tworefractive surfaces forming a spectacle lens has a progressiverefractive surface including a distance portion and a near portionhaving different focal powers, and a progressive portion having a focalpower progressively changed between said distance and near portions;coordinates are defined such that, assuming that said progressiverefractive surface of the lens assembled in each of spectacles is viewedfrom the front side of a user, the horizontal direction is taken as anX-axis; the vertical direction (direction between said distance and nearportions) is taken as a Y-axis; the depth direction is taken as aZ-axis; and a progressively change starting point located at the lowerend of said distance portion is taken as an origin (x, y, z)=(0, 0, 0);assuming that a radial inclination of an original progressive refractivesurface is taken as dz_(p) and a radial inclination of said progressiverefractive surface is taken as dz_(t), a relationship of dz_(t)=dz_(p)+δis established; and at said distance portion along a main meridian lineextending substantially in the Y-axis direction of said progressiverefractive surface, said δ is given by δ=g(r); at said near portionalong the main meridian line extending substantially in the Y-axisdirection of said progressive refractive surface, said δ is given byδ=h(r); and at other portions, said δ is given by δ=α·g(r)+β·h(r) whereα and β satisfy the relationship of α+β=1.0, 0≦α≦1, and 0≦β≦1; r is adistance from said progressively change starting point and is expressedby r=(x²+y²)^(½); and said g(r) and h(r) are each a function dependingonly on r and satisfy the relationship of g(r)≠h(r) and g(0)=0.
 8. Aprogressive power lens according to claim 7, wherein an angle formedbetween a straight line extending from the progressively change startingpoint to the outer peripheral portion of said progressive refractivesurface and said X-axis is taken as w, said α and β satisfy thefollowing equations (4) and (5): α=0.5+0.5 sin(w)  (4) β=0.5−0.5sin(w)  (5).
 9. A progressive power lens according to claim 7, whereinsaid g(r) and h(r) satisfy the following equations (6) and (7):$\begin{matrix}{{g(r)} = {\sum\limits_{n}{G_{n} \cdot \left( {r - r_{0}} \right)^{n}}}} & (6) \\{{h(r)} = {\sum\limits_{n}{H_{n} \cdot \left( {r - r_{0}} \right)^{n}}}} & (7)\end{matrix}$

where G_(n) and H_(n) are coefficients for determining g(r) and h(r),which are constants not depending on r for a certain progressiverefractive surface; and n is an integer of 2 or more.
 10. A progressivepower lens according to claim 7, wherein when 0≦r≦r₀, g(r) and h(r)satisfy the relationship of g(0)=0 and h(0)=0, and when r₀<r, g(r) andh(r) satisfy the following equations (6) and (7): $\begin{matrix}{{g(r)} = {\sum\limits_{n}{G_{n} \cdot \left( {r - r_{0}} \right)^{n}}}} & (6) \\{{h(r)} = {\sum\limits_{n}{H_{n} \cdot \left( {r - r_{0}} \right)^{n}}}} & (7)\end{matrix}$

where G_(n) and H_(n) are coefficients for determining g(r) and h(r),which are constants not depending on r for a certain progressiverefractive surface; and n is an integer of 2 or more.
 11. A progressivepower lens according to claim 10, wherein said r₀ is 7 mm or more andless than 12 mm.
 12. A progressive power lens according to claim 7,wherein said progressive refractive surface is provided on the eye side.13. A progressive power lens characterized in that at least one of tworefractive surfaces forming a spectacle lens has a progressiverefractive surface including a distance portion and a near portionhaving different focal powers, and a progressive portion having a focalpower progressively changed between said distance and near portions;coordinates are defined such that, assuming that said progressiverefractive surface of the lens assembled in each of spectacles is viewedfrom the front side of a user, the horizontal direction is taken as anX-axis; the vertical direction (direction between said distance and nearportions) is taken as a Y-axis; the depth direction is taken as aZ-axis; and a progressively change starting point located at the lowerend of said distance portion is taken as an origin (x, y, z)=(0, 0, 0);assuming that a radial curvature of an original progressive refractivesurface is taken as c_(p) and a radial curvature of said progressiverefractive surface is taken as c_(t), a relationship of c_(t)=c_(p)+δ isestablished; and at said distance portion along a main meridian lineextending substantially in the Y-axis direction of said progressiverefractive surface, said δ is given by δ=g(r); at said near portionalong the main meridian line extending substantially in the Y-axisdirection of said progressive refractive surface, said δ is given byδ=h(r); and at other portions, said δ is given by δ=α·g(r)+β·h(r) whereα and β satisfy the relationship of α+β=1.0, 0≦α≦1, and 0≦β≦1; r is adistance from said progressively change starting point and is expressedby r=(x²+y²)^(½); and said g(r) and h(r) are each a function dependingonly on r and satisfy the relationship of g(r)≠h(r) and g(0)=0.
 14. Aprogressive power lens according to claim 13, wherein an angle formedbetween a straight line extending from the progressively change startingpoint to the outer peripheral portion of said progressive refractivesurface and said X-axis is taken as w, said α and β satisfy thefollowing equations (4) and (5): α=0.5+0.5sin(w)  (4) β=0.5−0.5sin(w)  (5).
 15. A progressive power lens according to claim 13, whereinsaid g(r) and h(r) satisfy the following equations (6) and (7):$\begin{matrix}{{g(r)} = {\sum\limits_{n}{G_{n} \cdot \left( {r - r_{0}} \right)^{n}}}} & (6) \\{{h(r)} = {\sum\limits_{n}{H_{n} \cdot \left( {r - r_{0}} \right)^{n}}}} & (7)\end{matrix}$

where G_(n) and H_(n) are coefficients for determining g(r) and h(r),which are constants not depending on r for a certain progressiverefractive surface; and n is an integer of 2 or more.
 16. A progressivepower lens according to claim 13, wherein when 0≦r≦r₀, g(r) and h(r)satisfy the relationship of g(0)=0 and h(0)=0, and when r₀<r, g(r) andh(r) satisfy the following equations (6) and (7): $\begin{matrix}{{g(r)} = {\sum\limits_{n}{G_{n} \cdot \left( {r - r_{0}} \right)^{n}}}} & (6) \\{{h(r)} = {\sum\limits_{n}{H_{n} \cdot \left( {r - r_{0}} \right)^{n}}}} & (7)\end{matrix}$

where G_(n) and H_(n) are coefficients for determining g(r) and h(r),which are constants not depending on r for a certain progressiverefractive surface; and n is an integer of 2 or more.
 17. A progressivepower lens according to claim 16, wherein said r₀ is 7 mm or more andless than 12 mm.
 18. A progressive power lens according to claim 13,wherein said progressive refractive surface is provided on the eye side.19. A progressive power lens characterized in that at least one of tworefractive surfaces forming a spectacle lens has a progressiverefractive surface including a distance portion and a near portionhaving different focal powers, and a progressive portion having a focalpower progressively changed between said distance and near portions;coordinates are defined such that, assuming that said progressiverefractive surface of the lens assembled in each of spectacles is viewedfrom the front side of a user, the horizontal direction is taken as anX-axis; the vertical direction (direction between said distance and nearportions) is taken as a Y-axis; the depth direction is taken as aZ-axis; and a progressively change starting point located at the lowerend of said distance portion is taken as an origin (x, y, z)=(0, 0, 0);assuming that a coordinate of an original progressive refractive surfaceis taken as z_(p), and a coordinate of said progressive refractivesurface is taken as z_(t), a relationship expressed by the followingequation (2) using b_(p) defined by the following equation (1) isestablished; $\begin{matrix}{b_{p} = \frac{2z_{p}}{x^{2} + y^{2} + z_{p}^{2}}} & (1) \\{z_{t} = \frac{\left( {b_{p} + \delta} \right)r^{2}}{1 + \sqrt{1 - {\left( {b_{p} + \delta} \right)^{2}r^{2}}}}} & (2)\end{matrix}$

 at said distance portion along a main meridian line extendingsubstantially in the Y-axis direction of said progressive refractivesurface, said δ is given by δ=g(r); at said near portion along the mainmeridian line extending substantially in the Y-axis direction of saidprogressive refractive surface, said δ is given by δ=h(r); and at otherportions, said δ is given by δ=α·g(r)+βh(r) where α and β satisfy therelationship of α+β=1.0, 0≦α≦1, and 0≦β≦1; r is a distance from saidprogressively change starting point and is expressed by r=(x²+y²)^(½);and said g(r) and h(r) are each a function depending only on r andsatisfy the relationship of g(r)≠h(r) and g(0)=0.
 20. A progressivepower lens according to claim 19, wherein an angle formed between astraight line extending from the progressively change starting point tothe outer peripheral portion of said progressive refractive surface andsaid X-axis is taken as w, said α and β satisfy the following equations(4) and (5): α=0. 5+0.5 sin(w)  (4) β=0.5−0.5 sin(w)  (5).
 21. Aprogressive power lens according to claim 19, wherein said g(r) and h(r)satisfy the following equations (6) and (7): $\begin{matrix}{{g(r)} = {\sum\limits_{n}{G_{n} \cdot \left( {r - r_{0}} \right)^{n}}}} & (6) \\{{h(r)} = {\sum\limits_{n}{H_{n} \cdot \left( {r - r_{0}} \right)^{n}}}} & (7)\end{matrix}$

where G_(n) and H_(n) are coefficients for determining g(r) and h(r),which are constants not depending on r for a certain progressiverefractive surface; and n is an integer of 2 or more.
 22. A progressivepower lens according to claim 19, wherein when 0≦r≦r₀, g(r) and h(r)satisfy the relationship of g(0)=0 and h(0)=0, and when r₀<r, g(r) andh(r) satisfy the following equations (6) and (7): $\begin{matrix}{{g(r)} = {\sum\limits_{n}{G_{n} \cdot \left( {r - r_{0}} \right)^{n}}}} & (6) \\{{h(r)} = {\sum\limits_{n}{H_{n} \cdot \left( {r - r_{0}} \right)^{n}}}} & (7)\end{matrix}$

where G_(n) and H_(n) are coefficients for determining g(r) and h(r),which are constants not depending on r for a certain progressiverefractive surface; and n is an integer of 2 or more.
 23. A progressivepower lens according to claim 22, wherein said r₀ is 7 mm or more andless than 12 mm.
 24. A progressive power lens according to claim 19,wherein said progressive refractive surface is provided on the eye side.25. A progressive power lens characterized in that at least one of tworefractive surfaces forming a spectacle lens is configured as aprogressive refractive surface including a distance portion and a nearportion having different focal powers, and a progressive portion inwhich a focal power is progressively changed between said distance andnear portions; coordinates are defined such that, assuming that saidprogressive refractive surface of the lens assembled in each ofspectacles is viewed from the front side of a user, the horizontaldirection is taken as an X-axis; the vertical direction (directionbetween said distance and near portions) is taken as a Y-axis; the depthdirection is taken as a Z-axis; and a progressively change startingpoint located at the lower end of said distance portion is taken as anorigin (x, y, z)=(0, 0, 0); assuming that a coordinate of an originalprogressive refractive surface is taken as z_(p), and a coordinate ofsaid progressive refractive surface is taken as z_(t), a relationshipexpressed by the following equation (3) using b_(p) defined by thefollowing equation (1) is established; $\begin{matrix}{b_{p} = \frac{2z_{p}}{x^{2} + y^{2} + z_{p}^{2}}} & (1) \\{z_{t} = \frac{b_{p}r^{2}}{1 + \sqrt{1 - {\left( {1 + \delta} \right)b_{p}^{2}r^{2}}}}} & (3)\end{matrix}$

 at said distance portion along a main meridian line extendingsubstantially in the Y-axis direction of said progressive refractivesurface, said δ is given by δ=g(r); at said near portion along the mainmeridian line extending substantially in the Y-axis direction of saidprogressive refractive surface, said δ is given by δ=h(r); and at otherportions, said δ is given by δ=α·g(r)+β·h(r) where α and β satisfy therelationship of α+β=1.0, 0≦α≦1, and 0≦β≦1; r is a distance from saidprogressively change starting point and is expressed by r=(x²+y²)^(½);and said g(r) and h(r) are each a function depending only on r andsatisfy the relationship of g(r)≠h(r) and g(0)=0.
 26. A progressivepower lens according to claim 25, wherein an angle formed between astraight line extending from the progressively change starting point tothe outer peripheral portion of said progressive refractive surface andsaid X-axis is taken as w, said a and B satisfy the following equations(4) and (5): α=0.5+0.5 sin(w)  (4) β=0.5−0.5 sin(w)  (5).
 27. Aprogressive power lens according to claim 25, wherein said g(r) and h(r)satisfy the following equations (6) and (7): $\begin{matrix}{{g(r)} = {\sum\limits_{n}{G_{n} \cdot \left( {r - r_{0}} \right)^{n}}}} & (6) \\{{h(r)} = {\sum\limits_{n}{H_{n} \cdot \left( {r - r_{0}} \right)^{n}}}} & (7)\end{matrix}$

where G_(n) and H_(n) are coefficients for determining g(r) and h(r),which are constants not depending on r for a certain progressiverefractive surface; and n is an integer of 2 or more.
 28. A progressivepower lens according to claim 25, wherein when 0≦r≦r₀, g(r) and h(r)satisfy the relationship of g(0)=0 and h(0)=0, and when r₀<r, g(r) andh(r) satisfy the following equations (6) and (7): $\begin{matrix}{{g(r)} = {\sum\limits_{n}{G_{n} \cdot \left( {r - r_{0}} \right)^{n}}}} & (6) \\{{h(r)} = {\sum\limits_{n}{H_{n} \cdot \left( {r - r_{0}} \right)^{n}}}} & (7)\end{matrix}$

where G_(n) and H_(n) are coefficients for determining g(r) and h(r),which are constants not depending on r for a certain progressiverefractive surface; and n is an integer of 2 or more.
 29. A progressivepower lens according to claim 28, wherein said r₀ is 7 mm or more andless than 12 mm.
 30. A progressive power lens according to claim 25,wherein said progressive refractive surface is provided on the eye side.